This invention relates to seismic exploration and more particularly, to a method for correctly restoring seismic traces using cross-correlation.
In seismic exploration, it is common practice to deploy a large array of geophones on the surface of the earth and to record the vibrations of the earth at each geophone location to obtain a collection of seismic traces. The traces are sampled and recorded for further processing. When the vibrations so recorded are caused by a seismic source activated at a known time and location, the recorded data can be processed by a computer in known ways to produce an image of the subsurface. The image thus produced may be interpreted by geophysicists to detect the possible presence of valuable hydrocarbons.
Seismograms are most commonly recorded as digital samples which represent the amplitude of a received seismic signal as a function of time. Since seismograms are usually obtained along a line of exploration on the surface of the earth, the digital samples can be formed into x-t arrays with each sample in the array representing the amplitude of the seismic signal as a function of horizontal distance and time. When such array are visually reproduced, by plotting or the like, seismic sections are produced. A seismic section depicts the subsurface layering of a section of the earth. It is the principle tool which the geophysicist studies to determine the nature of the earth's subsurface formations. Before an array of seismic samples or traces can be converted into a seismic section for interpretation by geophysicists, the array must be extensively processed to remove noise and to make reflection events discernable.
A common problem during seismic data acquisition is the presence of seismic traces with no recorded data or seismic traces that clearly contain severe noise contamination. For example, the failure of one or more geophones intended to collect data can result in a seismic trace without data. Severe contamination, on the other hand, can result from numerous sources including random bursts of noise, multiple or intrabed reflections or ground roll.
Standard practice among geophysicists faced with seismic traces with no recorded data or severely contaminated seismic traces has been to exclude such traces, often referred to as "null" traces, from the otherwise satisfactory data set. The collected seismic data would be processed normally without the excluded data. When the missing trace was necessary for proper processing of the seismic data, prior attempts to restore the missing trace and create a trace with events consistent with nearby coherent events focused upon combining traces near the missing trace in the x-t domain to create the missing trace.
In the processing of seismograms, x-t arrays are sometimes transformed into arrays representing amplitude as a function of frequency and wave number. This is commonly referred to as a "frequency-wave number" or "f-k" transformation. In recent years the f-k transformation has proven useful as a tool for studying seismic data. F-k transforms are routinely used to represent seismic data collected by the aforementioned large arrays of sensors. Typically, the f-k representations are computed by Fast Fourier Transforms (hereafter referred to as FFTs). The resulting data representations are parameterized by frequencies, wave numbers (spatial frequencies), amplitudes and phases. In particular, for each frequency there is a collection of wave numbers, and for each frequency-wave number pair there is a complex number representative of an amplitude and a phase. Among various applications of this representation are spectra analysis (displaying the amplitude squared as a function of frequency and wave number) and filtering in the frequency-wave number domain.
In U.S. Pat. No. 4,218,765 issued to Kinkade, seismic traces are transformed to an f-k array. Filtering is then performed on the representations in the f-k domain. In U.S. Pat. No. 4,380,059 issued to Ruehle, multiple reflections are filtered from seismograms by transforming them into an f-k array representation of amplitude as a function of frequency and wave number. In Ruehle, the f-k array of the seismograms is filtered by weighting all the samples with the inverse of the f-k transform of the multiple reflections. In U.S. Pat. No. 4,594,693 issued to Pann et al, seismic trace interpolation is carried out by inserting zero amplitude traces between the seismic traces in a section where spatial aliasing is a problem. The traces are then transformed into an f-k array. The f-k array is filtered with a filter which rejects samples in a region of frequencies and wave numbers which exhibits aliasing. The filtered f-k array is then transformed into a seismic section representing amplitude as a function of time and distance.